Answer:
The equation of a line that passes through the points(-4, 4) and (2, 12) will be:
Hence, option A is true.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
Given the points
Finding the slope between (-4, 4) and (2, 12)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-4,\:4\right),\:\left(x_2,\:y_2\right)=\left(2,\:12\right)[/tex]
[tex]m=\frac{12-4}{2-\left(-4\right)}[/tex]
[tex]m=\frac{4}{3}[/tex]
Thus, the slope of the line m = 4/3
substituting (-4, 4) and m = 4/3 in the slope-intercept form of the line equation to determine the y-intercept b
y = mx+b
[tex]4=\frac{4}{3}\left(-4\right)+b[/tex]
switch sides
[tex]\frac{4}{3}\left(-4\right)+b=4[/tex]
[tex]-\frac{16}{3}+b=4[/tex]
Add 16 to both sides
[tex]-\frac{16}{3}+b+\frac{16}{3}=4+\frac{16}{3}[/tex]
[tex]b=\frac{28}{3}[/tex]
Thus, the y-intercept b = 28/3
now substituting b = 28/3 and m = 4/3 in the slope-intercept form of the line equation
y = mx+b
y = 4/3x + 28/3
Therefore, the equation of a line that passes through the points(-4, 4) and (2, 12) will be:
Hence, option A is true.
