A line passes through the points (–2,–1) and (19,14). Write its equation in slope-intercept form.

Step 1: Find the slope of the line

The slope of a line passing through the points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given points (-2, -1) and (19, 14) into the formula, we get:

m = (14 - (-1)) / (19 - (-2)) = 15 / 21 = 5/7

So, the slope of the line is 5/7.

Step 2: Use the slope-intercept form of a line

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

We already know that m = 5/7. To find b, we can substitute one of the given points and the slope into the equation and solve for b. Let's use the point (-2, -1):

-1 = (5/7)(-2) + b -1 = -10/7 + b -1 + 10/7 = b b = -7/7 + 10/7 = 3/7

So, the y-intercept is 3/7.

Step 3: Write the equation of the line

Substituting m = 5/7 and b = 3/7 into the slope-intercept form, we get:

y = (5/7)x + 3/7

So, the equation of the line in slope-intercept form is y = (5/7)x + 3/7.