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The equation of the line that goes through the points (-7,-2) and (-3,0) can be written in the form y=mx b

User Quaisha
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Final answer:

To write the equation of a line given two points, (-7,-2) and (-3,0), you first calculate the slope (m) and then use one point to solve for the y-intercept (b) in the equation y = mx + b. The equation is determined to be y = 0.5x + 1.5.

Step-by-step explanation:

The equation of a line that passes through two given points can be determined using the slope (m) and y-intercept (b) format of a linear equation, which is y = mx + b.

First, calculate the slope (m) which is defined as the change in the y-values (rise) divided by the change in the x-values (run). For the points (-7, -2) and (-3, 0), the slope is calculated as:

m = (0 - (-2)) / (-3 - (-7))
m = (0 + 2) / (-3 + 7)
m = 2 / 4
m = 0.5

With the slope identified, use either of the two points to determine the y-intercept (b) by substituting the values into the equation y = mx + b and solving for b:

0 = (0.5)(-3) + b
0 = -1.5 + b
b = 1.5

Thus, the equation of the line is y = 0.5x + 1.5.

User Crusy
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