Respuesta :
Answer:
• The slope of the line = -5/6
,• The y-intercept of the line = 1/2
Explanation:
Given the equation of the line below:
[tex]5x+6y=3[/tex]We are required to:
• Write the equation in ,slope-intercept form,.
,• Find the slope and y-intercept of the line.
The slope-intercept form of the equation of a straight line is:
[tex]\begin{equation} y=mx+b\text{ where }\begin{cases}m={slope} \\ b={y-intercept}\end{cases} \end{equation}[/tex]So, first, make y the subject of the given equation:
[tex]\begin{gathered} 5x+6y=3 \\ \text{Subtract 5x from both sides of the equation} \\ 5x-5x+6y=-5x+3 \\ 6y=-5x+3 \\ \text{Divide all through by 6} \\ \frac{6y}{6}=-\frac{5}{6}x+\frac{3}{6} \\ y=-\frac{5}{6}x+\frac{3}{6} \\ y=-\frac{5}{6}x+\frac{1}{2} \end{gathered}[/tex]Next, compare with the form given above:
[tex]\begin{gathered} Slope,m=-\frac{5}{6} \\ y-intercept,b=\frac{1}{2} \end{gathered}[/tex]• The slope of the line = -5/6
,• The y-intercept of the line = 1/2
