Maths-
General
Easy
Question
Find the gradient and y- Intercept of the line ![x plus 2 y equals 14](data:image/png;base64,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)
Hint:
Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, compare the equation with the standard form to get the slope and the y-intercept.
The correct answer is: we get Gradient = negative 1 half y-intercept = 7
Step by step solution:
The given equation of the line is
x + 2y = 14
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c
Rewriting the given equation, we have
2y = 14 - x
Dividing by 2, we get
![y equals 14 over 2 minus x over 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAjCAYAAAAUhR0LAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAe1JREFUeNrtmjFLw1AUhR8iItJFRBwcCqWIiLgXBxcRkVLcREREBCeH/gFxEEEcOrmIOIiIICIixUUcREQKIlLEQfBPOIi41HPJFULaYtLm2pf0HvigSQo9OXl57+amxtihIbAOnn1+PwsqRhVYR2DVZ3gJ8KpBNyc/4e2BFQ1aNuhxcBPgokiJLvR2jf2bfCzSQXeBMkhaEDTpCQy4tpfBbhxGNI2gtYDTjKSmQYE/T7rutEgHPQbuG5jPpXUNJrha6otD0CWQtjDoPPjmgRCLxbDyB60QLcxnPH3Mx7G8s2FEp8Al6OG6/jEuU4dNQfeDK0+wWX7oikTAQaeDVgRNJeY5GKxx7IQrEZWqjXQA5uqUL1saT3haAjuefbSivtVZTSvGzpLLes2AU8++DeP0iFUhikbti6eEeQfd/1RhhEkzvyvhuUqfrs8Fnp8lTLe97viJJ8WjuUMjkdEhyIFjsKhxyCnPZV5Zo5DVLM+tOY1CVhTwgwU+ftuPH8bp9VJTfcGyrJrySB2pjAUncWuc/m6Ct0eM83bFpp5vwx5HQdHiuy0ZgbUjCh596Us9yitjql/OqseQRW2AEi9A6lFIveACTKlHOaX4BNLqUU7DYN84PXH1KCT6Pxv1xjvVo6yKPFrUo7Ci0OMO7PEHK/m8ajPMlDMAAACrdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnk8L21pPjxtbz49PC9tbz48bWZyYWM+PG1uPjE0PC9tbj48bW4+MjwvbW4+PC9tZnJhYz48bW8+JiN4MjIxMjs8L21vPjxtZnJhYz48bWk+eDwvbWk+PG1uPjI8L21uPjwvbWZyYWM+PC9tYXRoPhasa3YAAAAASUVORK5CYII=)
Simplifying, we get
![y equals negative 1 half x plus 7](data:image/png;base64,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)
Comparing the above equation with , we get
![straight m equals negative 1 half semicolon straight c equals 7](data:image/png;base64,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)
Thus, we get
Gradient = ![negative 1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAjCAYAAABsFtHvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJ5JREFUeNpjYKA+UAPiWiC+wDAAYDEQpwHxf4YBBKOWj1o+avmo5TSzFB2PglEwuMB/IjA5ekZT/ygYfsAaiNcA8Scg/gVtOkfTy/KDQBwJxDxQvhYQH4WKDQiQB+JLAxkdPwbKYkto0NMdcADxSWhCpCsQBOINQOxGb4uVoBar0NtiDSCeDcRc9LZYHIhXATHLQCSwLVCfD7rGCFYAALTDPhrASBIsAAAAbHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4tPC9tbz48bWZyYWM+PG1uPjE8L21uPjxtbj4yPC9tbj48L21mcmFjPjwvbWF0aD7iC9uVAAAAAElFTkSuQmCC)
y-intercept = 7
We need to convert this equation in the slope-intercept form of the line, which is
Rewriting the given equation, we have
Dividing by 2, we get
Simplifying, we get
Comparing the above equation with , we get
Thus, we get
We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept =
, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula.
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