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Math  /  Algebra

QuestionGiven the points (−1,−5)(-1,-5) and (−4,16)(-4,16), answer the questions:
1. Slope is: −7✓-7 \checkmark
2. Point-Slope Form is: −7(x+5)=y+1∨-7(x+5)=y+1 \vee (Use the first point)
3. Slope-Intercept Form is: □\square

Studdy Solution

STEP 1

1. We have two points: (−1,−5)(-1, -5) and (−4,16)(-4, 16).
2. We will use the formula for slope to find the slope of the line passing through these points.
3. We will use the point-slope form of a line equation to express the line, using the first point.
4. We will convert the point-slope form to slope-intercept form.

STEP 2

1. Calculate the slope of the line.
2. Write the equation in point-slope form using the first point.
3. Convert the point-slope form to slope-intercept form.

STEP 3

Calculate the slope m m using the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (−1,−5)(-1, -5) and (−4,16)(-4, 16):
m=16−(−5)−4−(−1) m = \frac{16 - (-5)}{-4 - (-1)} m=16+5−4+1 m = \frac{16 + 5}{-4 + 1} m=21−3 m = \frac{21}{-3} m=−7 m = -7

STEP 4

Write the equation in point-slope form using the first point (−1,−5)(-1, -5) and the slope m=−7 m = -7 :
The point-slope form is:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
Substitute m=−7 m = -7 , x1=−1 x_1 = -1 , and y1=−5 y_1 = -5 :
y−(−5)=−7(x−(−1)) y - (-5) = -7(x - (-1)) y+5=−7(x+1) y + 5 = -7(x + 1)

STEP 5

Convert the point-slope form to slope-intercept form y=mx+b y = mx + b :
Start with:
y+5=−7(x+1) y + 5 = -7(x + 1)
Distribute the −7-7:
y+5=−7x−7 y + 5 = -7x - 7
Subtract 5 from both sides to solve for y y :
y=−7x−7−5 y = -7x - 7 - 5 y=−7x−12 y = -7x - 12
The slope-intercept form is:
y=−7x−12 y = -7x - 12
The slope-intercept form is y=−7x−12\boxed{y = -7x - 12}.

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