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Math  /  Algebra

QuestionQuestion 7 of 11 This quiz: 11 point(s) pos This question: 1 point(s)
Using the graph, find the equation of the line in slope-intercept form.
What is the slope-intercept form of the equation of the line? y=□\mathrm{y}=\square (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Studdy Solution

STEP 1

1. We are given two points on a line: (0,−2)(0, -2) and (4,2)(4, 2).
2. We need to find the equation of the line in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
3. The slope-intercept form requires calculating the slope and identifying the y-intercept.

STEP 2

1. Calculate the slope (mm) of the line using the given points.
2. Identify the y-intercept (bb) from the given points.
3. Write the equation of the line in slope-intercept form.

STEP 3

To find the slope (mm), use the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (x1,y1)=(0,−2)(x_1, y_1) = (0, -2) and (x2,y2)=(4,2)(x_2, y_2) = (4, 2):
m=2−(−2)4−0 m = \frac{2 - (-2)}{4 - 0}

STEP 4

Simplify the slope calculation:
m=2+24=44=1 m = \frac{2 + 2}{4} = \frac{4}{4} = 1
The slope mm is 1.

STEP 5

The y-intercept (bb) is the value of yy when x=0x = 0. From the point (0,−2)(0, -2), we see that the y-intercept is:
b=−2 b = -2

STEP 6

Now, write the equation of the line in slope-intercept form using the slope m=1m = 1 and y-intercept b=−2b = -2:
y=mx+b y = mx + b
Substitute mm and bb:
y=1x−2 y = 1x - 2
Simplify the equation:
y=x−2 y = x - 2
The slope-intercept form of the equation of the line is:
y=x−2 \boxed{y = x - 2}

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