Questions: Put the following equations in slope intercept forms. b) -4x+2y=-6 a) -2x+y=12 c) What is the slope of the line 3x+y=-12?

Transcript text: Put the following equations in slope intercept forms. b) $-4x+2y=-6$ a) $-2x+y=12$ c) What is the slope of the line $3x+y\equiv-12$?

Solution

Solution Steps

To convert the given equations into slope-intercept form, which is $ y = mx + b $, we need to solve each equation for $ y $. This involves isolating $ y $ on one side of the equation. For the third question, we need to identify the slope from the equation once it is in slope-intercept form.

Step 1: Convert the First Equation to Slope-Intercept Form

The first equation is given as $ -2x + y = 12 $. To convert it to slope-intercept form $ y = mx + b $, we solve for $ y $: \[ y = 2x + 12 \]

Step 2: Convert the Second Equation to Slope-Intercept Form

The second equation is $ -4x + 2y = -6 $. We isolate $ y $ to convert it to slope-intercept form: \[ 2y = 4x - 6 \implies y = 2x - 3 \]

Step 3: Find the Slope of the Third Equation

The third equation is $ 3x + y = -12 $. We rearrange it to find the slope: \[ y = -3x - 12 \] From this equation, we can see that the slope $ m $ is $ -3 $.