Question

Rewrite the given equation in slope-intercept form and the graph the line.2x + 5y - 10= 0What is the equation in slope intercept form?(Use integers or simplified fractions for any numbers in the equation)

Answer 1

y=-(2/5)x+2

Explanation:

Given the equation of the line:

`2x+5y-10=0`

The slope-intercept form of a line is given as y=mx+b.

Thus, make y the subject of the given equation.

`\begin{gathered} 5y=-2x+10 \\ \text{Divide all through by 5} \\ y=-(2)/(5)x+(10)/(5) \\ y=-(2)/(5)x+2 \end{gathered}`

The slope-intercept form of the equation is y=-(2/5)x+2.

Next, the lines are graphed using the intercepts.

When y=0

`\begin{gathered} 0=-(2)/(5)x+2\implies(2)/(5)x=2 \\ \text{Multiply both sides by }(5)/(2) \\ (2)/(5)*(5)/(2)x=2*(5)/(2) \\ x=5 \end{gathered}`

• The x-intercept is (5,0)

,

• From the slope-intercept form, the y-intercept is (0,2).

Join the two points using a straight line as shown below: