Final answer:
The slope of the line represented by the equation 5x+3y=15 is -5/3. The y-intercept is 5, at which point the line crosses the y-axis at (0, 5). The x-intercept is 3, where the line crosses the x-axis at (3, 0).
Step-by-step explanation:
To find the slope, y-intercept, and x-intercept of the equation 5x+3y=15, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, solve for y to get the equation into y = mx + b form:
First, solve for y to get the equation into y = mx + b form:
3y = -5x + 15
y = (-5/3)x + 5
To find the slope (m), look at the coefficient of x:
The slope (m) is -5/3.
To find the y-intercept (b), look at the constant term:
The y-intercept (b) is 5, meaning the line crosses the y-axis at (0, 5).
To find the x-intercept, set y to 0 and solve for x:
0 = (-5/3)x + 5
5/3x = 5
x=3
The x-intercept is 3, meaning that the line crosses the x-axis at (3, 0).