Graph the line with the given point and slope. Find the two coordinates.

Question

The line through ​(-2​, 1​) with slope 4/5.

Answer 1

To graph the line through (-2, 1) with slope 4/5, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

In this case, the given point is (-2, 1) and the slope is 4/5. Plugging these values into the point-slope form, we get:

y - 1 = (4/5)(x - (-2))
y - 1 = (4/5)(x + 2)
y - 1 = (4/5)x + 8/5

Now, we can rearrange the equation to get it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

y = (4/5)x + 8/5 + 1
y = (4/5)x + 13/5

Using this equation, we can now plot the line on a coordinate plane.

To find two coordinates on the line, we can choose arbitrary x-values and plug them into the equation to solve for the corresponding y-values. For example, we can choose x = 0 and x = 5.

When x = 0:
y = (4/5)(0) + 13/5
y = 13/5

So one coordinate on the line is (0, 13/5).

When x = 5:
y = (4/5)(5) + 13/5
y = 4 + 13/5
y = (20/5) + 13/5
y = 33/5

So another coordinate on the line is (5, 33/5).

Now, we can plot these two coordinates on the graph of the line.