Math / Algebra

QuestionA line has a slope of 6 and passes through the point $(-4,-20)$ . Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line, specifically in slope-intercept form ( $y = mx + b$ ), given its slope and a point it passes through. Watch out! Don't mix up the x and y coordinates of the given point!
Also, remember that slope-intercept form is $y = mx + b$ , not $y = bx + m$ .

STEP 2

1. Plug in the known values
2. Solve for the y-intercept
3. Write the final equation

STEP 3

Remember that slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
We're given that the slope is $m = 6$ , and the line passes through the point $(-4, -20)$ , which means when $x = -4$ , $y = -20$ .

STEP 4

Let's plug these values into our equation: $-20 = 6 \cdot (-4) + b$

STEP 5

Now, let's simplify and solve for $b$ : $-20 = -24 + b$

STEP 6

To isolate $b$ , we can add $24$ to both sides of the equation: $-20 + 24 = -24 + b + 24$ $4 = b$ So, our y-intercept is $b = 4$ .

STEP 7

We now know both the slope, $m = 6$ , and the y-intercept, $b = 4$ .
Let's plug these back into the slope-intercept form, $y = mx + b$ : $y = 6x + 4$

STEP 8

The equation of the line in slope-intercept form is $y = 6x + 4$ .

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QuestionA line has a slope of 6 and passes through the point $(-4,-20)$ . Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

STEP 2

1. Plug in the known values
2. Solve for the y-intercept
3. Write the final equation

STEP 3

Remember that slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
We're given that the slope is $m = 6$ , and the line passes through the point $(-4, -20)$ , which means when $x = -4$ , $y = -20$ .

STEP 4

Let's plug these values into our equation: $-20 = 6 \cdot (-4) + b$

STEP 5

Now, let's simplify and solve for $b$ : $-20 = -24 + b$

STEP 6

To isolate $b$ , we can add $24$ to both sides of the equation: $-20 + 24 = -24 + b + 24$ $4 = b$ So, our y-intercept is $b = 4$ .

STEP 7

We now know both the slope, $m = 6$ , and the y-intercept, $b = 4$ .
Let's plug these back into the slope-intercept form, $y = mx + b$ : $y = 6x + 4$

STEP 8

The equation of the line in slope-intercept form is $y = 6x + 4$ .

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QuestionA line has a slope of 6 and passes through the point (−4,−20)(-4,-20)(−4,−20). Write its equation in slopeintercept form.Write your answer using integers, proper fractions, and improper fractions in simplest form. □\square□

Studdy Solution

STEP 1

STEP 2

1. Plug in the known values2. Solve for the y-intercept3. Write the final equation

STEP 3

Remember that slope-intercept form is y=mx+by = mx + by=mx+b, where mmm is the **slope** and bbb is the **y-intercept**.We're given that the slope is m=6m = 6m=6, and the line passes through the point (−4,−20)(-4, -20)(−4,−20), which means when x=−4x = -4x=−4, y=−20y = -20y=−20.

STEP 4

Let's **plug these values** into our equation: −20=6⋅(−4)+b-20 = 6 \cdot (-4) + b−20=6⋅(−4)+b

STEP 5

Now, let's **simplify and solve for** bbb: −20=−24+b-20 = -24 + b−20=−24+b

STEP 6

To **isolate** bbb, we can **add** 242424 to both sides of the equation: −20+24=−24+b+24-20 + 24 = -24 + b + 24−20+24=−24+b+24 4=b4 = b4=bSo, our **y-intercept** is b=4b = 4b=4.

STEP 7

We now know both the **slope**, m=6m = 6m=6, and the **y-intercept**, b=4b = 4b=4.Let's **plug these back** into the slope-intercept form, y=mx+by = mx + by=mx+b: y=6x+4y = 6x + 4y=6x+4

STEP 8

The equation of the line in slope-intercept form is y=6x+4y = 6x + 4y=6x+4.

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QuestionA line has a slope of 6 and passes through the point $(-4,-20)$ . Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

1. Plug in the known values
2. Solve for the y-intercept
3. Write the final equation

Remember that slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
We're given that the slope is $m = 6$ , and the line passes through the point $(-4, -20)$ , which means when $x = -4$ , $y = -20$ .

Let's plug these values into our equation: $-20 = 6 \cdot (-4) + b$

Now, let's simplify and solve for $b$ : $-20 = -24 + b$

To isolate $b$ , we can add $24$ to both sides of the equation: $-20 + 24 = -24 + b + 24$ $4 = b$ So, our y-intercept is $b = 4$ .

We now know both the slope, $m = 6$ , and the y-intercept, $b = 4$ .
Let's plug these back into the slope-intercept form, $y = mx + b$ : $y = 6x + 4$

The equation of the line in slope-intercept form is $y = 6x + 4$ .