Sure! Let's work through these problems step by step.
### Problem 14
We are given the point [tex]\((-7, 13)\)[/tex] and the slope [tex]\(m = -2\)[/tex]. We need to write the equation of the line in slope-intercept form, which is [tex]\(y = mx + b\)[/tex].
1. Start with the point-slope form of the line:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
2. Plug in the given point [tex]\((-7, 13)\)[/tex] and the slope [tex]\(m = -2\)[/tex] into the formula:
[tex]\[y - 13 = -2(x + 7)\][/tex]
3. Simplify the equation to get it into the slope-intercept form:
[tex]\[
y - 13 = -2x - 14 \\
y = -2x - 14 + 13 \\
y = -2x - 1
\][/tex]
So, the equation of the line in slope-intercept form is:
[tex]\[ y = -2x - 1 \][/tex]
### Problem 15
We are given the point [tex]\((-4, 6)\)[/tex] and the slope [tex]\(m = -\frac{3}{4}\)[/tex]. We need to write the equation of the line in slope-intercept form.
1. Start with the point-slope form of the line:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
2. Plug in the given point [tex]\((-4, 6)\)[/tex] and the slope [tex]\(m = -\frac{3}{4}\)[/tex] into the formula:
[tex]\[y - 6 = -\frac{3}{4}(x + 4)\][/tex]
3. Simplify the equation to get it into the slope-intercept form:
[tex]\[
y - 6 = -\frac{3}{4}x - 3 \\
y = -\frac{3}{4}x - 3 + 6 \\
y = -\frac{3}{4}x + 3
\][/tex]
So, the equation of the line in slope-intercept form is:
[tex]\[ y = -\frac{3}{4}x + 3 \][/tex]
### Summary
14. The equation of the line with the point [tex]\((-7, 13)\)[/tex] and slope [tex]\(-2\)[/tex] is:
[tex]\[ y = -2x - 1 \][/tex]
15. The equation of the line with the point [tex]\((-4, 6)\)[/tex] and slope [tex]\(-\frac{3}{4}\)[/tex] is:
[tex]\[ y = -\frac{3}{4}x + 3 \][/tex]
### Problem 16 and 17
You did not provide information on problems 16 and 17. Please provide the necessary details to solve those problems.
