What is the equation in slope-intercept form of the line that passes through (-4,2) and (12,6)

To use the slope-intercept form, we need a slope.

Recall that the slope of a line m = (y2 - y1) / (x2 - x1). We are given the coordinates of two points, both of which lie on the line (the line passes through them): (-4,2) and 12,6).

So given these two points, let's let x1 = -4 and y1 = 2; and let's let x2 = 12 and y2 = 6. Substituting these values into the equation for the slope of a line, we get

m = (6 - 2) / [12 - (-4)] = 4 / 16, or m = 1/4

So now we have the slope, and we can use the point-slope form of the equation of a line to help us determine the y-intercept. The point-slope form is y - y1 = m * (x - x1)

Substituting our slope m = 1/4 and either one of the points (let's say the first point), we have

y - 2 = 1/4 * [x - (-4)] = 1/4 * (x + 4)

Now add 2 to both sides of this equation, and we have y = 1/4 * (x + 4) + 2

Using the distributive law, we can further reduce this to y = 1/4 * x + 1 + 2, or y = 1/4 * x + 3

Finally, the y-intercept of a line is where the line intersects the y-axis or, mathematically speaking, where the x-coordinate is equal to zero. So let's let x = 0 in the equation above, and solve for y. Substituting x = 0 into the equation for our line, we now have

y = 1/4 * 0 + 3 = 3

So our y-intercept is 3 (three). Now we can write the equation for our line in the slope-intercept form:

y = m * x + b, where m is the slope and b is the y-intercept. Substituting for m and b, we get

y = 1/4 * x + 3.

So the equation in slope-intercept form of the line that passes through points (-4,2) and (12,6) is

y = 1/4 * x + 3

(To check your answer, substitute either one of the points into the equation...)

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