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Math  /  Algebra

Question/activitybuilder/instance/674efbba6950e871bcac89db/student/674f475712e503d27285c524\#screenld=b41ae290-cc56-429e-810e-07bd955554a2 f Values and Graph π{ }^{\pi} n
Write the equation of a line in slope intercept form GIVEN A GRAPH. Enter all three into the answer box.
Slope: \qquad Y-intercept: \qquad Equation: \qquad □\square Submit

Studdy Solution

STEP 1

1. The problem requires us to find the equation of a line in slope-intercept form, which is y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept.
2. We are given a set of points from a table, which we can use to determine the slope and y-intercept.
3. The points provided are (0,20)(0, 20), (3,11)(3, 11), (6,2)(6, 2), and (9,−7)(9, -7).

STEP 2

1. Calculate the slope m m using two points from the table.
2. Determine the y-intercept b b using one of the points.
3. Write the equation of the line in slope-intercept form.
4. Verify the equation with the other points.

STEP 3

To find the slope m m , we use the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Let's use the points (0,20)(0, 20) and (3,11)(3, 11).
m=11−203−0=−93=−3 m = \frac{11 - 20}{3 - 0} = \frac{-9}{3} = -3

STEP 4

The y-intercept b b is the value of y y when x=0 x = 0 . From the table, when x=0 x = 0 , y=20 y = 20 .
So, b=20 b = 20 .

STEP 5

Now, write the equation of the line in slope-intercept form:
y=−3x+20 y = -3x + 20

STEP 6

Verify the equation with the other points (6,2)(6, 2) and (9,−7)(9, -7).
For (6,2)(6, 2):
y=−3(6)+20=−18+20=2 y = -3(6) + 20 = -18 + 20 = 2
For (9,−7)(9, -7):
y=−3(9)+20=−27+20=−7 y = -3(9) + 20 = -27 + 20 = -7
Both points satisfy the equation, confirming its correctness.
The solution is:
Slope: −3 -3 Y-intercept: 20 20 Equation: y=−3x+20 y = -3x + 20

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