Answer:
[tex]y=\frac{3}{4}x+\frac{11}{2}[/tex]
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through (-2, 4) and (2, 7).
The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
First, let's find the slope of the line.
The slope, calculated from two points is given as the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
We have two points, which is needed to find the slope, but let's label their values to avoid confusion.
[tex]x_1=-2\\y_1=4\\x_2=2\\y_2=7[/tex]
Now substitute those values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{7-4}{2--2}[/tex]
Simplify
m=[tex]\frac{7-4}{2+2}[/tex]
m=[tex]\frac{3}{4}[/tex]
So the slope of the line is [tex]\frac{3}{4}[/tex].
Substitute that value as m in y=mx+b
y=[tex]\frac{3}{4}x+b[/tex]
Now we need to find b
As the equation passes through both (-2, 4) and (2, 7), we can substitute the values of either one of them in the equation to solve for b
Taking (-2, 4) for example,
Substitute -2 as x and 4 as y:
4=[tex]\frac{3}{4}(-2)+b[/tex]
Multiply
4=[tex]-\frac{3}{2}[/tex]+b
Add -3/2 to both sides
[tex]\frac{11}{2} = b[/tex]
Substitute that value into the equation
y=[tex]\frac{3}{4}x+\frac{11}{2}[/tex]
Hope this helps!
