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Question

Question: How can you find the slope and intercept of \[3y = 7\] ?...

How can you find the slope and intercept of 3y=73y = 7 ?

Explanation

Solution

Since we need to find the slope and intercept so we need to convert the equation into slope-intercept form by solving yy and any linear equation has the form of y=mx+cy = mx + c where mm stands as slope which can be found by finding two distinct points and cc is the yy intercept where graph hits yy axis.

Formula used:
Since slope mm depicts how steep the line is with respect to horizontal. So if in the line two points found are (x1,y1)({x_1},{y_1}) and (x2,y2)({x_2},{y_2}) so slope comes out to be
m=y2y1x2x1m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}
The point where line crosses why yy axis is the yy intercept cc

Complete step by step solution:
As the given equation is 3y=73y = 7
Since we know that y=mx+cy = mx + c is the slope intercept form of a line where mm is equal to slope and cc is the yy intercept (0,c)(0,c)
Now by dividing both the sides of the equation by 33 we will put the given equation in slope-intercept form.

33y=73 y=73 y=0x+73  \Rightarrow \dfrac{3}{3}y = \dfrac{7}{3} \\\ \Rightarrow y = \dfrac{7}{3} \\\ \Rightarrow y = 0x + \dfrac{7}{3} \\\

So they have a slope=0slope = 0 and this is a horizontal line
It means slope=m=0slope = m = 0 and y intercept c=(0,73)c = \left( {0,\dfrac{7}{3}} \right)

Note: While solving the above equation we need to convert the equation given in the slope intercept form and later on after finding the value of mm and cc then pick a point on line and check if it satisfies the equation by plugging it in. In the above equation the slope is horizontal as the value of mm comes out to be 00. For verification we put value of yy in the equation 3y=73y = 7 and we found that

3×73=7 7=7  \Rightarrow 3 \times \dfrac{7}{3} = 7 \\\ \Rightarrow 7 = 7 \\\

It means LHS=RHSLHS = RHS.