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.