Question

What is the slope and intercept for `y=2x+3` and how would you graph it?

Answer 1

See answers below

Explanation:

The given equation of line:

`y=2x+3`

Comparing above equation with the standard slope-intercept form `y=mx+c`, we get

Slope: `m=2`

Now, given equation can be re-written as

`2x-y=-3`

`x/{-3/2}+y/3=1`

Comparing above equation with intercept form: `x/a+y/b=1`, we get

x-intercept: `a=-3/2`

y-intercept: `b=3`

Now, the given straight line intersects the coordinate axes at `(-3/2, 0)` & `(0, 3)`. Specify these points on XY-plane & join them by a straight line to get plot.

Answer 2

Here is the solution

Explanation:

Assign a value to x to find y value

If x is 1, `y=5`

Assign another value to x

If x is 2, `y=7`

Slope formula `=(Delta y) / (Delta x) = (7-5)/(2-1) = 2`

If x is zero `y=3`

If y is zero, `x=-3/2`

The graph is below (it is a linear function)

graph{(2x) + 3 [-8.88, 11.12, -3.96, 6.04]}