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

#### Explanation:

The given equation of line:

$y = 2 x + 3$

Comparing above equation with the standard slope-intercept form $y = m x + c$, we get

Slope: $m = 2$

Now, given equation can be re-written as

$2 x - y = - 3$

$\frac{x}{- \frac{3}{2}} + \frac{y}{3} = 1$

Comparing above equation with intercept form: $\frac{x}{a} + \frac{y}{b} = 1$, we get

x-intercept: $a = - \frac{3}{2}$

y-intercept: $b = 3$

Now, the given straight line intersects the coordinate axes at $\left(- \frac{3}{2} , 0\right)$ & $\left(0 , 3\right)$. Specify these points on XY-plane & join them by a straight line to get plot.

Jul 26, 2018

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 $= \frac{\Delta y}{\Delta x} = \frac{7 - 5}{2 - 1} = 2$

If x is zero $y = 3$

If y is zero, $x = - \frac{3}{2}$

The graph is below (it is a linear function)

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