1. **State the problem:** Find the equation of the line in slope-intercept form that is parallel to the line $2x + 5y = 10$ and has the same $x$-intercept as the line $3x + 4y = 15$. 2. **Find the slope of the given line $2x + 5y = 10$:** Rewrite in slope-intercept form $y = mx + b$: $$5y = -2x + 10$$ $$y = -\frac{2}{5}x + 2$$ So, the slope $m = -\frac{2}{5}$. 3. **Find the $x$-intercept of the line $3x + 4y = 15$:** At $x$-intercept, $y=0$: $$3x + 4(0) = 15 \implies 3x = 15 \implies x = 5$$ So, the $x$-intercept is $(5, 0)$. 4. **Write the equation of the line parallel to $2x + 5y = 10$ passing through $(5,0)$:** Parallel lines have the same slope, so slope $m = -\frac{2}{5}$. Use point-slope form: $$y - y_1 = m(x - x_1)$$ Substitute $x_1=5$, $y_1=0$: $$y - 0 = -\frac{2}{5}(x - 5)$$ Simplify: $$y = -\frac{2}{5}x + 2$$ 5. **Final answer:** The equation in slope-intercept form is $$y = -\frac{2}{5}x + 2$$