slope-intercept form for the line that passes through (1, 1) and is perpendicular to the graph of 3x + 2y = -7

Answer 1

Being perpendicular to a line means the solpe is the negative reciprocal of that line. So, if the line has a slope of 3/4, then the line perpendicular to it has a slope of -4/3.

To find the slope of the line 3x + 2y = -7, we can put it in slope-intercept form.

3x + 2y = -7 subtract 3x from both sides to get:

2y = -3x - 7 divide both sides by 2 to get:

y = -3/2x - 7/2

so the slope of this line is -3/2.

The slope of the line perpendicular to it is 2/3.

So we are looking for a line passing through (1. 1) that has a slope of 2/3. Using the point slope form (y - y₁) = m(x - x₁), the equation of this line is (y - 1) = 2/3(x - 1). But we are being asked for the slope-intercept form (y = mx + b) so we can algebraically manipulate it to get it into the correct form:

(y - 1) = 2/3(x - 1) Multiply this out to get:

y - 1 = 2/3x - 2/3 Add 1 to each side to get:

y = 2/3x + 1/3

Answer 2

The line, l1, defined by the equation 3x + 2y = -7 has a slope of -3/2; you can put it into y = mx + b form to see that.

A line, l2, which is perpendicular to l1 has a slope of 2/3 which is the negative reciprocal of the slope of l1.

Since we know a point, (1,1), and the slope of l2, 2/3, we can put the point into a slope formula and set it equal to the slope of l2, generating an equation:

(y-1)/(x-1) = 2/3

Then you can manipulate that equation into any other form.

You are being asked for slope-intercept form which is y = (slope)*x + intercept or y= mx + b.