The equation of the line 5x+2y−2=05𝑥+2𝑦−2=0 can be written in slope-intercept form y=mx+c𝑦=𝑚𝑥+𝑐. The slope m𝑚 of the line is __________. A.m=25𝑚=25B.m=52𝑚=52C.m=−25𝑚=−25D.m=−5
Question
The equation of the line 5x+2y−2=05𝑥+2𝑦−2=0 can be written in slope-intercept form y=mx+c𝑦=𝑚𝑥+𝑐. The slope m𝑚 of the line is __________. A.m=25𝑚=25B.m=52𝑚=52C.m=−25𝑚=−25D.m=−5
Solution
The slope-intercept form of a linear equation is y = mx + c, where m is the slope and c is the y-intercept.
To find the slope (m), we need to rearrange the given equation 5x + 2y - 2 = 0 into the slope-intercept form.
Step 1: Subtract 5x from both sides of the equation to isolate the y term. This gives us 2y = -5x + 2.
Step 2: Divide every term by 2 to solve for y. This gives us y = -5/2x + 1.
So, the slope m of the line is -5/2.
Therefore, the correct answer is C. m = -5/2.
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