Question

graph the line that has a slope of \\(\frac{2}{5}\\) and includes the point (5, 2) click to select points on the graph.

Explanation:

Step1: Recall the point - slope form of a line

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. We know that $m=\frac{2}{5}$ and the point $(x_1,y_1)=(5,2)$. Substitute these values into the point - slope formula:
$y - 2=\frac{2}{5}(x - 5)$

Step2: Simplify the equation

First, distribute the $\frac{2}{5}$ on the right - hand side:
$y - 2=\frac{2}{5}x-\frac{2}{5}\times5$
$y - 2=\frac{2}{5}x - 2$
Then, add 2 to both sides of the equation:
$y=\frac{2}{5}x$

Step3: Find other points on the line

We can find other points by plugging in values of $x$ and solving for $y$.

• When $x = 0$, $y=\frac{2}{5}(0)=0$, so the point $(0,0)$ is on the line.
• When $x = 10$, $y=\frac{2}{5}(10) = 4$, so the point $(10,4)$ is on the line.
• When $x=- 5$, $y=\frac{2}{5}(-5)=-2$, but since our graph has non - negative axes (from the given grid), we can use positive $x$ values.

To graph the line, we start with the point $(5,2)$. The slope $\frac{2}{5}$ means that for every 5 units we move to the right (increase in $x$ by 5), we move up 2 units (increase in $y$ by 2). So from $(5,2)$, if we move 5 units to the right (to $x = 5 + 5=10$), we move up 2 units (to $y=2 + 2 = 4$), giving the point $(10,4)$. If we move 5 units to the left (to $x=5 - 5 = 0$), we move down 2 units (to $y = 2-2=0$), giving the point $(0,0)$.

Answer:

To graph the line with slope $\frac{2}{5}$ passing through $(5,2)$, we can use the points $(5,2)$, $(0,0)$ and $(10,4)$ (among others). Plot the point $(5,2)$ first. Then, from $(5,2)$, move 5 units right and 2 units up to get to $(10,4)$, or 5 units left and 2 units down to get to $(0,0)$. Then draw a straight line through these points.