Answer:
[tex]y = -\frac{5}{2}x + \frac{7}{2}[/tex] (Slope-Intercept Form)
[tex]m = -\frac{5}{2}[/tex] (Slope)
[tex]b = \frac{7}{2}[/tex] (Y-Intercept)
Step-by-step explanation:
1.) The first step to convert an equation in standard form ([tex]ax + by = c[/tex]) to slope-intercept form ([tex]y = mx + b[/tex]) is to isolate the variable y on one side of the equation through transposing the terms with the variable x and the constants on the other side of the equation.
⇒ [tex]5x + 2y = 7[/tex]
⇒ [tex]5x + 2y - (5x) = 7 - (5x)[/tex]
⇒ [tex]2y = 7 - 5x[/tex]
⇒ [tex]2y = -5x + 7[/tex]
2.) If the coefficient or integer in front of the term with the variable [tex]y[/tex] has a value greater than one, divide that integer to both sides of the equation to solve for the variable [tex]y[/tex].
⇒ [tex]2y = -5x + 7[/tex]
⇒ [tex]\frac{2y}{2} = \frac{-5x + 7}{2}[/tex]
⇒ [tex]\bold{y = -\frac{5}{2}x + \frac{7}{2}}[/tex]
⇒ [tex]\bold{m = -\frac{5}{2}}[/tex] and [tex]\bold{b = \frac{7}{2}}[/tex]
3.) Therefore, the standard form equation [tex]5x + 2y = 7[/tex], converted into slope intercept form is [tex]y = -\frac{5}{2}x + \frac{7}{2}[/tex]. And the slope ([tex]m[/tex]) and y-intercept ([tex]b[/tex]) are [tex]-\frac{5}{2}[/tex] and [tex]\frac{7}{2}[/tex] respectively.
I hope this helps you understand this concept in Mathematics.
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