What is the equation of the line that has a slope of 2 and goes through (1,5)?

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Answer 1 · 2018-03-10T04:48:31

$y = 2 x + 3$ $y=2x+3$

Use the point-slope formula:

$y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$

Where:

$(x_{1}, y_{1})$ $(x_1,y_1)$ is a point on the graph

$m$ $m$ is the slope

From the information given to us,

$(x_{1}, y_{1}) \to (1, 5)$ $(x_1,y_1)->(1,5)$

$m = 2$ $m=2$

So...

$y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$
$↓$ $" "darr$
$y - (5) = 2 (x - (1))$ $y-(5)=2(x-(1))$

To get into $y = m x + b$ $y=mx+b$ form, all we do is solve for $y$ $y$

$y - (5) = 2 (x - (1))$ $y-(5)=2(x-(1))$

$y - 5 = 2 x - 2$ $y-5=2x-2$

$y - 5 + 5 = 2 x - 2 + 5$ $y-5+5=2x-2+5$

$y = 2 x + 3$ $y=2x+3$

The graph of this is shown below:

graph{2x+3 [-10, 10, -5, 5]}