Question

lesson practice
a. graph a line that has a slope of 2 and passes through the point (5, 6).
b. graph a line that has a slope of 0 and passes through the point (-1, 1).
c. write the equation of a line that has a slope of 6 and passes through the point (7, 9) in point-slope form.
d. write the equation of a line that passes through the points (2, -3) and (7, 4) in slope-intercept form.

Explanation:

Step1: (Part a) Recall point-slope form

Point-slope form: $y - y_1 = m(x - x_1)$
Substitute $m=2$, $(x_1,y_1)=(5,6)$:
$y - 6 = 2(x - 5)$
Simplify to slope-intercept: $y = 2x - 4$
To graph: Plot $(5,6)$, use slope $\frac{2}{1}$ (rise 2, run 1) to find another point, draw line.

Step2: (Part b) Recognize slope 0 line

Slope 0 = horizontal line: $y = k$
Substitute $y$-value of $(-1,1)$:
$y = 1$
To graph: Draw a horizontal line through $y=1$, passing through $(-1,1)$.

Step3: (Part c) Apply point-slope formula

Point-slope form: $y - y_1 = m(x - x_1)$
Substitute $m=6$, $(x_1,y_1)=(7,9)$:
$y - 9 = 6(x - 7)$

Step4: (Part d) Calculate slope first

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute $(2,-3)$ and $(7,4)$:
$m = \frac{4 - (-3)}{7 - 2} = \frac{7}{5}$

Step5: (Part d) Find intercept, write form

Use slope-intercept $y = mx + b$, substitute $m=\frac{7}{5}$ and $(2,-3)$:
$-3 = \frac{7}{5}(2) + b$
$-3 = \frac{14}{5} + b$
$b = -3 - \frac{14}{5} = -\frac{15}{5} - \frac{14}{5} = -\frac{29}{5}$
Final equation: $y = \frac{7}{5}x - \frac{29}{5}$

Answer:

a. Graph the line $y=2x-4$ (plot $(5,6)$, use slope 2 to extend the line)
b. Graph the horizontal line $y=1$ (passes through $(-1,1)$)
c. $y - 9 = 6(x - 7)$
d. $y = \frac{7}{5}x - \frac{29}{5}$