Let's take this problem step-by-step:
If a line is parallel to each other:
⇒ their slope must be equal
Thus the line parallel to: [tex]y=\frac{3}{4}x-4[/tex]
⇒ that line's slope: 3/4
The point-slope form is: [tex](y-y_1)=m(x-x_1)[/tex]
Let's put that line into the point-slope form:
[tex](y-7)=\frac{3}{4}(x+1)[/tex] <== Answer
Hope that helps!
#LearnwithBrainly
Answer:
[tex]y - 7 = \frac{3}{4} (x+1)[/tex]
Step-by-step explanation:
We are given the equation y = 3/4x-4, and we want to write an equation of a line that is parallel to y=3/4x-4, and that also passes through (-1, 7), in point-slope form.
Point-slope form is written as [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope, and [tex](x_1, y_1)[/tex] is a point
If two lines are parallel to each other, it means they have the same slope.
The line y = 3/4x-4 is written in the form slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 3/4 is in the place of where m is, 3/4 is the slope of this line.
It is also the slope of our new line.
So we can substitute 3/4 as m in [tex]y-y_1=m(x-x_1)[/tex].
[tex]y-y_1=\frac{3}{4} (x-x_1)[/tex]
Now, we need to replace the values of [tex]x_1[/tex] and [tex]y_1[/tex] with a point.
Since we are given (-1, 7), and that it passes through the line, it means that we can use its values in the equation.
Note that we have subtraction in this equation, so when we use a negative number, we still write the subtraction sign in front of the minus sign the negative number has. Just because the number is already negative doesn't mean we ignore the minus sign the formula gives.
[tex]y-7=\frac{3}{4} (x--1)[/tex]
We can simplify this equation, as --1 is the same as +1.
[tex]y-7=\frac{3}{4} (x+1)[/tex]
