Question

Consider the following linear equation.3x + y = 2Step 1 of 2: Determine the slope and the y-intercept (entered as an ordered pair) of the equationabove. Reduce all fractions to lowest terms.AnswerKeypadKeyboard ShortcutsSlope:y-intercept:

Answer 1

slope: -3

y-intercept: 2

Explanation

Step 1

the equation of a line is given by:

$y=mx+b$

where m is the slope and b is the y-intercept

hence, to find the slope and y-intercept values need to isolate x and reorder, so

$\begin{gathered} 3x+y=2 \\ \text{subtracty 3x in both sides} \\ 3x+y-3x=2-3x \\ y=2-3x \\ \text{reorder} \\ y=-3x+2 \end{gathered}$

hence

$\begin{gathered} y=mx+b\Rightarrow y=-3x+2 \\ so \\ \text{slope}=m=-3 \\ y-\text{intercept}=b=2 \end{gathered}$

therefore, the answer is

slope: -3

y-intercept: 2

Step 2

graph the line.to graph the line we need to find 2 points of the line, then draw a line that passes trougth those points, so

a) point 1,

for x= 0

replace

$\begin{gathered} y=-3x+2 \\ y=-3(0)+2 \\ y=0+2=2 \\ so \\ \text{ Point1 ( 0,2)} \end{gathered}$

b) for x= 2

replace

$\begin{gathered} y=-3x+2 \\ y=-3(2)+2 \\ y=-6+2=-4 \\ so \\ \text{ Point2 ( 2,-4)} \end{gathered}$

c) finally, draw a line that passes through (0,2) and (2,-4)

I hope this helps you