Respuesta :
To answer this question, we need to know that the x- and y-intercepts are:
• The x-intercept: (5, 0). The point where the line passes through the x-axis.
,• The y-intercept: (0, 3). The point where the line passes through the y-axis.
To find the equation of the line, we can use the two-point form equation of the line, and then we will find the standard form of the line, which is of the form:
[tex]Ax+By=C[/tex]We still need to label both points:
• (5, 0) ---> x1 = 5, y1 = 0.
,• (0, 3) ---> x2 = 0, y2 = 3.
The two-point form of the line is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Then, substituting these values into this equation, we have:
[tex]y-0=\frac{3-0}{0-5}(x-5)\Rightarrow y=\frac{3}{-5}(x-5)\Rightarrow y=-\frac{3}{5}(x-5)[/tex]Then, we have:
[tex]y=-\frac{3}{5}x+\frac{3}{5}\cdot5\Rightarrow y=-\frac{3}{5}x+3[/tex]This is the slope-intercept form of the line. To find the standard form of the line, we can multiply the equation by 5 as follows:
[tex]5(y=-\frac{3}{5}x+3)\Rightarrow5y=5(-\frac{3}{5})x+5\cdot3\Rightarrow5y=-3x+15[/tex]Adding 3x to both sides of the equation, we have:
[tex]5y+3x=-3x+3x+15\Rightarrow5y+3x=15[/tex]Finally, the standard form of the line is given by 3x + 5y = 15.
