Question

The equation of the line that passes through the points (-2, 3) and (2, 7) can be found using the point-slope form of a linear equation: − 1= ( − 1)y−y1=m(x−x1) Where: 1=−2x1=−2 1=3y1=3 2=2x2=2 2=7y2=7 Now, calculate the slope (m): = 2− 1 2− 1=7−32−(−2)=44=1m=x2−x1y2−y1=2−(−2)7−3=44=1 Now you can use the point-slope form with one of the given points: −3=1( −(−2))y−3=1(x−(−2)) Simplify it: −3= +2y−3=x+2 Now, isolate y: = +2+3y=x+2+3 = +5y=x+5 So, the equation of the line is = +5y=x+5.

Answer 1

The equation of a line passing through the points (-2, 3) and (2, 7) is found by calculating the slope and applying it to the point-slope form, resulting in the final slope-intercept form of y = x + 5.

Step-by-step explanation:

The student's question pertains to finding the equation of a line that passes through two given points. The calculation of the slope (m) and the construction of the equation in the point-slope form are at the core of finding this linear equation. Following this method, we find that the slope (m) of our line is the rise over run, which is the change in y divided by the change in x.

In the case of the given points (-2, 3) and (2, 7), the slope is calculated as follows:

m = (y2 - y1) / (x2 - x1)
= (7 - 3) / (2 - (-2))
= 4 / 4
= 1

Now, using one of the points and the slope, we can formulate the line's equation in point-slope form, and then simplify it to the slope-intercept form:

y - 3 = 1(x - (-2))
y = x + 5

The equation of our line in slope-intercept form is y = x + 5, which clearly reveals that the line has a slope of 1 and a y-intercept of 5.