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Write an equation of the line that passes through (9,8) and is parallel to the line y=-5x-4

2 Answers

3 votes

Answer:

▸ y = 5x - 37

Step-by-step explanation:

We are asked to write an equation for a line that:

  • passes through (9,8)
  • is parallel to y = 5x - 4

Parallel lines have the same slopes. So, the line that's parallel to y = 5x - 4 has the same slope as the line y = 5x - 4, which is 5. However, the y-intercepts are different.

We know the slope of the new line, but we also know the point that it passes through. So, we can use our point-slope formula:


\boldsymbol{y-y_1=m(x-x_1)}

Substitute our values:


\boldsymbol{y-8=5(x-9)}

Distribute 5:


\boldsymbol{y-8=5x-45}

Add 8 to both sides:


\boldsymbol{y=5x-45+8}

Simplify:


\boldsymbol{y=5x-37}

Result:

▸ y = 5x - 37

User Snow Bunting
by
8.5k points
4 votes

Answer:The equation of a line parallel to another line will have the same slope. The given line has a slope of -5. So, the line parallel to it will also have a slope of -5.

The general equation of a line is given by y=mx+c

where m is the slope and c is the y-intercept.

We know that the line passes through the point (9,8). Substituting these values into the equation gives us:

8=−5∗9+c

Solving for c, we get:

c=8+5∗9=53

So, the equation of the line that passes through (9,8) and is parallel to the line y=-5x-4 is:

y=−5x+53

Step-by-step explanation:

User Razdi
by
8.6k points

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