Question

(3, 2), y = x + 5 Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation.

Answer 1

Answer:

y = x - 1

Step-by-step explanation:

Since the line is parallel to y = x + 5, it will have the same slope, which is 1.

Plug in the slope and the given point into y = mx + b, and solve for b:

y = mx + b

2 = 1(3) + b

2 = 3 + b

-1 = b

Then, plug in the slope and b into the equation:

y = mx + b

y = x - 1

So, the equation is y = x - 1

Answer 2

The equation of the line in slope-intercept form is: y = x - 1

What is Slope-intercept Equation?

• The equation of a line, where m is the slope and b is the y-intercept, is modelled by the equation, y = mx + b.
• Slope of parallel lines will be the same.

Thus, the slope (m) of the line that is parallel to y = x + 5 will be 1.

Write the equation of the line by substituting (a, b) = (3, 2) and m = 1 into y - b = m(x - a):

y - 2 = 1(x - 3)

• Rewrite in slope-intercept form:

y - 2 = x - 3

y = x - 3 + 2

y = x - 1

Therefore, the equation of the line in slope-intercept form is: y = x - 1.

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