Question

graph a line parallel to y=3x-1 that contains (2,3).

Answer 1

The line equation is y = 3x - 1 and the point (2, 3).

The equation y = 3x - 1 is adjusted in the slope - intercept form of equation or y = mx + b where m is slope and b is y - intercept.

Therefore slope of given line is 3.

If two lines are parallel, then they have the same slope.

So, the parallel line through (2, 3) has a slope of 3.

To find the y - intercept, substitute the values of (x, y) = (2, 3) and m = 3 in the slope - intercept from of equation y = mx + b and solve for b.

3 = 3(2) + b

3 = 6 + b

6 + b = 3

Subtract 6 from each side.

b = 3 - 6

b = - 3.

Substitute the values of m = 3 and b = - 3 in the slope - intercept form of equation.

y = mx + b ⇒ y = 3x - 3.

The equation of parallel line is y = 3x - 3.

slope = 3 and y - intercept is - 3.

y - intercept is - 3, so the line crosses the y - axis at (0, - 3)

Using slope find the next point.

Slope = rise/run = 3/1

Start at point (0, - 3), move 3 units up and 1 unit right, then plot the point (1, 0).

Draw a line through these points.

Graph :