The required equation of line in the slope-intercept form will be [tex]y=-\dfrac{5}{2}x+4[/tex].
The given equation of line is [tex]5x+2y=8[/tex].
It is required to write the equation of a line in the slope-intercept form which has infinitely many solutions in the system of equation with the given line.
The system of equations has infinitely many solutions when the equations are the same or all of their coefficients are in the same ratio.
So, the other equation could be,
[tex]k(5x+2y)=8k\\5x+2y=8[/tex]
Now, the equation in slope-intercept form can be written as,
[tex]5x+2y=8\\2y=-5x+8\\y=-\dfrac{5}{2}x+4[/tex]
where the slope of the line is [tex]-\dfrac{5}{2}[/tex] and the y-intercept is 4.
Therefore, the required equation of line in the slope-intercept form will be [tex]y=-\dfrac{5}{2}x+4[/tex].
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https://brainly.com/question/11824567
