Mathematics

Mathematics

Problem

For the line 5x+2y−10=05x + 2y - 10 = 0, which ordered triple (slope, x-intercept, y-intercept)(\text{slope},\,x\text{-intercept},\,y\text{-intercept}) is correct? a) (−25, 5, 2)\left(-\dfrac{2}{5},\,5,\,2\right) b) (−52, 2, 5)\left(-\dfrac{5}{2},\,2,\,5\right) c) (52, −2, 5)\left(\dfrac{5}{2},\,-2,\,5\right) d) (−52, −2, 5)\left(-\dfrac{5}{2},\,-2,\,5\right)
Intuitive explanation

The key is to rewrite the line equation in a form that reveals its slope and intercepts directly. Convert to slope-intercept form y=mx+by = mx + b to read off the slope mm and yy-intercept bb, then set y=0y = 0 to find where the line crosses the xx-axis. This systematic approach avoids confusion and gives you all three values at once.

Intuitive explanation

The key is to rewrite the line equation in a form that reveals its slope and intercepts directly. Convert to slope-intercept form y=mx+by = mx + b to read off the slope mm and yy-intercept bb, then set y=0y = 0 to find where the line crosses the xx-axis. This systematic approach avoids confusion and gives you all three values at once.

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